First measurements concerning rhytmic circuit inertia and disparition
written by Daniel Devatman Hromada for Joelle Provasi
as memoire M1 for EPHE SVT CNA
The experiment consisted of three tasks: during first a spontaneous motor tempo (SMT) was
measured; during the second a child had to synchronise to stimuli with 600ms interstimuli interval
(ISI); third task was a continuation/induction task – after being attuned to a 600ms ISI, a child was
instructed to continue tapping the same rhythm (IRI) even after stimuli was turned off. This text
concerns only the 3rd task in relation to data obtained by SMT measurements of the 1st task.
Crucial for understanding of our method is the concept of “IRI falling into the SMT attractor state”.
We say that subject’s IRI have fallen into the SMT attractor state when an IRI cannot be
distinguished from SMT. For practical purposes we define that IRI cannot be distinguished from
SMT state when the arithmetic mean of 3 subsequent IRIs is lesser than SMT, e.g. IRI<SMT. As
may be noticed from Figure 1, XXXX of our subjects have sooner or later fallen into SMT attractor
state during the continuation task.
And more, we can demand when this event have
occurred. Thus we label the beginning of 3tapped sequence specified above as “the moment
of passing of an SMT attractor threshold”.
Having a sequence of taps where 1 denotes first
tap, 2 second etc. a number N will be called an
“SMT attractor’s threshold passing’s sequence
number” if and only if:
mean(IRIN IRIN+1 +IRIN+2) < SMT
It is important to understand that once we know
SMT attractor’s passing sequence number, we
can easily calculate the time interval between the
beginning of the continuation sequence T0 and a
passing of an SMT attractor as a sum of all the
IRIs occurred between 0 (e.g. the and of a ISI
sequence) and N. This is due to construction of
our experiment – we can be more or less sure
that measurement of IRI2 starts in the very
moment when IRI1 ends, with minimal
-computer processing speed related- temporal
gap between them. We formalize:
N

T N =∑ IRI i
i=0

Since the beginning of the continuation sentence
marks as well the end of an ISI sequence, this
summing up of all IRIs which occurred before
passing the threshold can be interpreted as a time
interval between the moment when ISI was
turned off and a moment when a subject’s IRI
have fallen into the SMT attractor state. For the
purpose of this article we’ll say that TN denotes

SEX AGE TRAINING
f
4m
g
4m
f
5m
g
5m
g
4n
f
5n
g
5n
f
4m
g
4m
f
4n
g
4n
f
5n
g
4m
f
5m
g
5m
f
4n
g
4n
g
5n
f
4m
g
4m
f
5m
f
4n
g
4n
g
5n
f
4m
g
4m
f
5m
g
5m
f
4n
g
4n
f
4m
f
5n
g
5n
f
4m
f
5n

SMT
360
401
538
568
503,5
558
548,5
542
461
540
377,5
566
567
484
431
402
481
484
552
432
501,5
558
400
528
379
525,5
537
564
514
428
564
444
445
446
486

IFI
12411
9171
29118
11137
11047
18006
15385
7583
12321
15353
15742
14984
10288
18042
13898
11161
2680
4586
7270
15847
15990
19966
518
14321
14659
13638
11458
9838
1988
7088
2332
16595
8890
16747
14354

Tableau 1: SMTs and ISI’s fadeaway intervals
- IFIs (in miliseconds) of 35 subjects whose
previously measured SMT<550 as related to
their respective sex/age/musical training
factors

the ISI’s fadeaway interval (IFI) . Table 1 shows different IFI’s for 27 subjects whose SMT<550 and
hence could in comparison with IRI=600 produce measurable results.
Results
A three-factored (sex,age,musical training) ANOVA was run over measured IFIs of 35 subjects
whose SMT<550 This analysis revealed a significant main effect of age (p<0.039) and indicated a
possible effect of sex (p<0.0691). No interaction nor effect of musical training was observed. An
unilateral Student's test suggests (p<0.02) that a mean IFI of 5years old (14440ms) is greater than
mean IFI of 4 year olds (10390ms)
Discussion
We use the term “SMT attractor” because we think that SMT can be described as an equilibrium
state of child's cognitive system in particular of global oscillatory module . We consider an SMT to
be an attractor because
1) it's much more probable that a child will change its IRI from ISI to SMT than the other way
around1
2) SMT cyclic equilibrium once attained, child's rhytmic cognitive system will tend to rest in it
until next perturbation by external stimuli.
Since we had defined IFI as a time interval between the moment when a child was attuned
to ISI and a moment when it passed SMT's atractor threshold, we can say that this interval describes
the time needed for an irreversible deletion of an initial ISI. We can say that when IRI is departing
from ISI and approaching SMT, ISI is rewritten by SMT. More IRI approaches SMT, more
information about initial ISI is lost, most it is improbable that IRI will come back to ISI.
Thus we think that IFI can be an interesting notion for measuring certain characteristics of
rhytmic memory and maybe a first step towards a new method of studying memory in general. For
initial ISI’s gradual fadeout can be either interpreted as both
● temporal interval needed for an irreversible disparition/deletion of a certain rhythmic
behavior pattern
● temporal interval during which a certain rhythmic behaviour pattern “resists” its deletion.
If we adhere to the second interpretation, we can say that an IFI measure can be an
interesting clue to what we call inertia of a given behaviour pattern/neural circuit. What our data
shown us is, rhytmic behaviour patterns of 4year olds have lesser inertia than those of 5years old. In
other words, neural rhytmic loops of 5 years old resist better the tendance to be deleted from the
rhytmic memory than those of younger children. Simply said, more a child is older, more the
contents of its memory have a capacity to become “frozen” - more solid is an energetic equilibrium
of all neural loops concerned . We think that these conclusions are consistent with other results of
child memory development research
Bibliography ???
The functional emergence of prefrontally-guided working memory systems in four- to eight-year-old
children

1 In the language of dynamical systems: SMT drains the basin of attraction composed of all other IRI states

Illustration 1: Diagrams representing an execution of a continuation task by 41 children subjects.
X axis is the tap's sequence number, Y axis signifies the IRI value. Observed left-to-right gradual
decrease of IRI can be interpreted as a fall into an SMT attractor state.